Induced gravity with complex metric field

Abstract

The possible existence of a complex metric tensor field is studied. We show that an effective scalar field is induced by an overall phase component of the complex metric tensor. The corresponding gauge field is shown to be a tachyon. Possible implications of this scalar field to the no hair theorem in a spherically symmetric space is also analyzed. We also study its impact on the evolution of the early universe.

4 pages, some typos corrected